Try replacing the F+R struts, strut mounts, front anti-roll bar bushings, and you'll see a marked improvement.
Also consider going with a stiffer front sway (anti-roll) bar and stiffer bushings. It'll do a lot to improve the side-side handling. Shocks do improve the side-side handling, but it doesn't sound like you want to go too hard. Check out tdiparts for struts. VWvortex has a lot of good links for suspension tuning , I don't know much about suspension tuning, it's a real trial-error art.
I would avoid stiff shocks, changing major suspension parts other than the front sway bar and bushings, and shocks. Maybe you can get some low mileage parts off a GTI or GLI? Just remember that the springs are different partly due to the different weight supported by them, it'll turn out slightly differently on a GTI or GLI than on your car. The other parts are mostly the same.
Some people suggest raising the car, I am not a huge fan. It can tighten the suspension and give you more ground clearance but it'll also raise your center of gravity.
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